Arbitrage and Duality in Nondominated Discrete-Time Models
AbstractWe consider a nondominated model of a discrete-time financial market where stocks are traded dynamically and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum over the martingale measures. Moreover, we obtain a nondominated version of the Optional Decomposition Theorem.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1305.6008.
Date of creation: May 2013
Date of revision: Feb 2014
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-04 (All new papers)
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